The inverse properties

Additive inverses

When two numbers are added together and the result is the additive identity, 0, the numbers are called
additive inverses of each other. For example, when 3 is added
to
−3 the result is 0, that is,
3+(−3)=0 . The numbers 3 and
−3 are additive inverses of each other.

Multiplicative inverses

When two numbers are multiplied together and the result is the multiplicative identity, 1, the numbers are called
multiplicative inverses of each other. For example, when 6 and
16 are multiplied together, the result is 1, that is,
6⋅16=1 . The numbers 6 and
16 are multiplicative inverses of each other.

We summarize the inverse properties as follows.

The inverse properties

If
a is any real number, then there is a unique real number
−a , such that
a+(−a)=0and−a+a=0The numbers
a and
−a are called
additive inverses of each other.

If
a is any nonzero real number, then there is a unique real number
1a such that
a⋅1a=1and1a⋅a=1The numbers
a and
1a are called
multiplicative inverses of each other.

Expanding quantities

When we perform operations such as
6(a+3)=6a+18 , we say we are
expanding the quantity
6(a+3) .

Exercises

Use the commutative property of addition and multiplication to write expressions for an equal number for the following problems. You need not perform any calculations.

fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.

Tarell

what is the actual application of fullerenes nowadays?

Damian

That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.

Tarell

Join the discussion...

what is the Synthesis, properties,and applications of carbon nano chemistry

Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.